1. Field Of Invention
This invention relates to artificial intelligence and to signal processing. In particular, the invention relates to the classification or filtering of information derived from primitive perception for use in developing a description of observed events in the absence of prior knowledge about the significance of events.
Traditionally, phenomena such as physical objects, terrain, and the like are considered to have unique, "true" lengths, areas, volumes, tangents, and other metric properties. This "true" value is the one obtained in the limit, as some factor of scale of measurement goes to zero. For example, arc length is defined as the limit of a polygonal approximation to a curve, as the length of each side of the polygon goes to zero.
The traditional notion of length doesn't hold for a broad class of irregular physical structures and processes. The problem is that when measuring the length of, e.g., a coastline by polygonal approximation, the measured length increases without apparent bound as the length of the polygonal side decreases (intuitively, because the smaller "yardstick" conforms to ever smaller sub-bays and sub-peninsulas.) Since the limiting value is undefined (or at least uninteresting), there can be no meaningful evaluation of metric properties without reference to the scale at which the properties are measured (i.e., the length of the "yardstick," or some other parameter of scale.)
It has therefore been assumed that the choice of scale and range of scale is fundamentally a tradeoff between resolution and noise. A small scale observation can resolve closely spaced events but is sensitive to noise. A large scale observation blurs events but is less sensitive to noise. The scale threshold, which is often predetermined based on empirical factors for which there is no analytical model, frequently determines how events are defined. The inherent ambiguity in scale parameterization is often a serious problem, because there is usually no simple principled basis for setting the scale parameter. Thus, if a query is directed to how long, how wide, or how steeply inclined is an irregular physical structure or the function of a physical measurement process, there is no single "correct" answer, since the answer changes, sometimes significantly, as the scale of measurement is changed. The ambiguity of scale cannot in general be eliminated by any simple process; rather the problem as herein formulated is to reduce the ambiguity as much as possible and to present the alternatives in an organized, discrete, symbolic fashion.
One technique for circumventing the problem without really solving it has been simply to select a scale of observation based on a guess at a model for the relationship between the data collected and the conclusions desired. There nevertheless remains a need for a technique for analyzing raw continuous data to develop a discrete symbolic description which can be manipulated according to known analytical signal models.
It is to be understood that measurement of any sort requires at least some primitive scale parameterization in order to maintain a measurement of properties in a range of scale. The size of any neighborhood determines the scale of description. For example, a linear scale may be able to usefully present events for display with respect to an independent variable between zero and ten with a resolution of one part in one hundred. This represents a uniformly weighted scale range of three orders of magnitude. Various property measurement techniques may be applied within any scale range as, for example, local fitting of analytical functions to data, spatial averaging and the like. Each property measurement technique has in common the continuous parameterization by scale of some local measure on the signal.
As used herein a scale-dependent measure on a signal might be defined as a function of the signal, a function of a location on the signal, and a function of a parameter of scale, such that values in the signal contribute to the function's output to a diminishing degree as they become more distant from the original location; and such that the rate at which the values' contributions diminish with distance decreases as the value of the parameter of scale increases. A scale-dependent measure is for example the result of convolving the signal with a gaussian, using the gaussian's standard deviation ("width") as the parameter of scale.
2. Description Of The Prior Art
There are no known analytical signal models capable of describing different physical events which occur at different physical scales, namely, events which appear like noise within one scale but correspond to interesting events within another scale. More than twenty years of research in machine vision has yielded compelling evidence that even problems once considered to be comparatively simple, such as edge detection, are beyond the capabilities of known signal processing techniques as measured against performance of the human visual system. In fact, the human visual system is often capable of perceiving and distinguishing meaningful relationships among abstract, non-visual variables in graphs, scattergrams, histograms, perspective surface plots, radar returns and like non-visual event description and to organize data in terms of distinguished points, including peaks, steps and inflections, with far greater accuracy than any known signal processing technique.
The scale management problem has been addressed extensively in computer vision as for example the works of Rosenfeld, A. and Thurston, M. "Edge and Curve Detection for Visual Scene Analysis," IEEE Transactions on Computers, Vol. C-20, pp. 562-569 (May 1971), Marr, D. and Poggio, T. "A Computational Theory of Human Stereo Vision," Proc. R. Soc. Lond., B. 204 (1979) pp. 301-328, and Marr, D. and Hildreth, E. C. "Theory of Edge Detection," M.I.T. Artificial Intelligence Memo Number 518, Cambridge, Massachusetts (April 1979). However, the scale management problem has not been solved satisfactorily. For example, in Marr's works, it is suggested that multiple descriptions at a fixed series of mask sizes be used for observing events, the mask sizes corresponding to different scales and scale ranges. Marr was unable to integrate these multiple descriptions effectively. His choice of mask sizes or scale was largely motivated by neural physiological considerations.